LMFDB - Embedded newform 243.2.g.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			199.1
Character	$\chi$	$=$	243.199
Dual form			243.2.g.a.127.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71221 - 1.81484i) q^{2} +(-0.245679 + 4.21814i) q^{4} +(-1.39804 + 0.163408i) q^{5} +(-2.85083 - 1.43174i) q^{7} +(4.25325 - 3.56890i) q^{8} +(2.69030 + 2.25743i) q^{10} +(1.87624 + 4.34961i) q^{11} +(2.07522 + 0.491837i) q^{13} +(2.28284 + 7.62523i) q^{14} +(-5.36597 - 0.627192i) q^{16} +(-0.520249 + 2.95048i) q^{17} +(1.23380 + 6.99724i) q^{19} +(-0.345808 - 5.93730i) q^{20} +(4.68131 - 10.8525i) q^{22} +(2.70239 - 1.35719i) q^{23} +(-2.93740 + 0.696176i) q^{25} +(-2.66061 - 4.60832i) q^{26} +(6.73968 - 11.6735i) q^{28} +(0.631591 - 2.10966i) q^{29} +(3.14652 + 2.06950i) q^{31} +(1.41830 + 1.90511i) q^{32} +(6.24541 - 4.10767i) q^{34} +(4.21955 + 1.53579i) q^{35} +(-6.31317 + 2.29781i) q^{37} +(10.5863 - 14.2199i) q^{38} +(-5.36304 + 5.68449i) q^{40} +(-2.90628 + 3.08048i) q^{41} +(0.474097 - 0.636822i) q^{43} +(-18.8082 + 6.84563i) q^{44} +(-7.09015 - 2.58060i) q^{46} +(-4.83370 + 3.17917i) q^{47} +(1.89725 + 2.54844i) q^{49} +(6.29289 + 4.13890i) q^{50} +(-2.58448 + 8.63275i) q^{52} +(-4.83254 + 8.37020i) q^{53} +(-3.33382 - 5.77435i) q^{55} +(-17.2350 + 4.08478i) q^{56} +(-4.91010 + 2.46595i) q^{58} +(0.636054 - 1.47454i) q^{59} +(0.0674875 + 1.15872i) q^{61} +(-1.63170 - 9.25383i) q^{62} +(-0.847235 + 4.80491i) q^{64} +(-2.98162 - 0.348502i) q^{65} +(1.71558 + 5.73045i) q^{67} +(-12.3177 - 2.91935i) q^{68} +(-4.43754 - 10.2874i) q^{70} +(-2.74773 - 2.30562i) q^{71} +(8.55952 - 7.18229i) q^{73} +(14.9796 + 7.52304i) q^{74} +(-29.8185 + 3.48528i) q^{76} +(0.878675 - 15.0863i) q^{77} +(-3.21730 - 3.41014i) q^{79} +7.60435 q^{80} +10.5667 q^{82} +(10.2659 + 10.8812i) q^{83} +(0.245199 - 4.20991i) q^{85} +(-1.96748 + 0.229966i) q^{86} +(23.5034 + 11.8038i) q^{88} +(-3.17449 + 2.66371i) q^{89} +(-5.21193 - 4.37333i) q^{91} +(5.06091 + 11.7325i) q^{92} +(14.0460 + 3.32896i) q^{94} +(-2.86831 - 9.58083i) q^{95} +(-12.5027 - 1.46135i) q^{97} +(1.37652 - 7.80666i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.71221	−	1.81484i	−1.21071	−	1.28328i	−0.947949	−	0.318423i	$-0.896847\pi$
$2$	−1.71221	−	1.81484i	−1.21071	−	1.28328i	−0.262766	−	0.964860i	$-0.584635\pi$
$3$		0			0
$3$		0			0
$4$	−0.245679	+	4.21814i	−0.122839	+	2.10907i
$5$	−1.39804	+	0.163408i	−0.625224	+	0.0730783i	−0.422805	−	0.906221i	$-0.638954\pi$
$5$	−1.39804	+	0.163408i	−0.625224	+	0.0730783i	−0.202419	+	0.979299i	$0.564880\pi$
$6$		0			0
$7$	−2.85083	−	1.43174i	−1.07751	−	0.541147i	−0.180691	−	0.983540i	$-0.557834\pi$
$7$	−2.85083	−	1.43174i	−1.07751	−	0.541147i	−0.896822	+	0.442393i	$0.854130\pi$
$8$	4.25325	−	3.56890i	1.50375	−	1.26180i
$9$		0			0
$10$	2.69030	+	2.25743i	0.850749	+	0.713863i
$11$	1.87624	+	4.34961i	0.565707	+	1.31146i	0.925615	+	0.378468i	$0.123549\pi$
$11$	1.87624	+	4.34961i	0.565707	+	1.31146i	−0.359908	+	0.932988i	$0.617192\pi$
$12$		0			0
$13$	2.07522	+	0.491837i	0.575563	+	0.136411i	0.508081	−	0.861309i	$-0.330355\pi$
$13$	2.07522	+	0.491837i	0.575563	+	0.136411i	0.0674826	+	0.997720i	$0.478503\pi$
$14$	2.28284	+	7.62523i	0.610116	+	2.03793i
$15$		0			0
$16$	−5.36597	−	0.627192i	−1.34149	−	0.156798i
$17$	−0.520249	+	2.95048i	−0.126179	+	0.715596i	0.854422	+	0.519580i	$0.173912\pi$
$17$	−0.520249	+	2.95048i	−0.126179	+	0.715596i	−0.980601	+	0.196016i	$0.937200\pi$
$18$		0			0
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	0.712157	+	0.702020i	$0.247718\pi$
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	−0.429103	+	0.903255i	$0.641170\pi$
$20$	−0.345808	−	5.93730i	−0.0773250	−	1.32762i
$21$		0			0
$22$	4.68131	−	10.8525i	0.998059	−	2.31376i
$23$	2.70239	−	1.35719i	0.563488	−	0.282994i	−0.144166	−	0.989554i	$-0.546050\pi$
$23$	2.70239	−	1.35719i	0.563488	−	0.282994i	0.707654	+	0.706559i	$0.249754\pi$
$24$		0			0
$25$	−2.93740	+	0.696176i	−0.587480	+	0.139235i
$26$	−2.66061	−	4.60832i	−0.521789	−	0.903765i
$27$		0			0
$28$	6.73968	−	11.6735i	1.27368	−	2.20608i
$29$	0.631591	−	2.10966i	0.117284	−	0.391754i	−0.879109	−	0.476621i	$-0.841861\pi$
$29$	0.631591	−	2.10966i	0.117284	−	0.391754i	0.996392	+	0.0848670i	$0.0270465\pi$
$30$		0			0
$31$	3.14652	+	2.06950i	0.565132	+	0.371693i	0.799694	−	0.600408i	$-0.204995\pi$
$31$	3.14652	+	2.06950i	0.565132	+	0.371693i	−0.234562	+	0.972101i	$0.575366\pi$
$32$	1.41830	+	1.90511i	0.250723	+	0.336779i
$33$		0			0
$34$	6.24541	−	4.10767i	1.07108	−	0.704459i
$35$	4.21955	+	1.53579i	0.713233	+	0.259596i
$36$		0			0
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.804076	−	0.594527i	$-0.797339\pi$
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.233803	+	0.972284i	$0.575117\pi$
$38$	10.5863	−	14.2199i	1.71733	−	2.30677i
$39$		0			0
$40$	−5.36304	+	5.68449i	−0.847971	+	0.898797i
$41$	−2.90628	+	3.08048i	−0.453884	+	0.481089i	−0.913390	−	0.407085i	$-0.866545\pi$
$41$	−2.90628	+	3.08048i	−0.453884	+	0.481089i	0.459506	+	0.888175i	$0.348027\pi$
$42$		0			0
$43$	0.474097	−	0.636822i	0.0722991	−	0.0971145i	−0.764503	−	0.644621i	$-0.777015\pi$
$43$	0.474097	−	0.636822i	0.0722991	−	0.0971145i	0.836802	+	0.547506i	$0.184423\pi$
$44$	−18.8082	+	6.84563i	−2.83544	+	1.03202i
$45$		0			0
$46$	−7.09015	−	2.58060i	−1.04538	−	0.380489i
$47$	−4.83370	+	3.17917i	−0.705067	+	0.463730i	−0.850729	−	0.525605i	$-0.823839\pi$
$47$	−4.83370	+	3.17917i	−0.705067	+	0.463730i	0.145662	+	0.989334i	$0.453469\pi$
$48$		0			0
$49$	1.89725	+	2.54844i	0.271035	+	0.364063i
$50$	6.29289	+	4.13890i	0.889949	+	0.585328i
$51$		0			0
$52$	−2.58448	+	8.63275i	−0.358402	+	1.19715i
$53$	−4.83254	+	8.37020i	−0.663800	+	1.14973i	0.315809	+	0.948823i	$0.397724\pi$
$53$	−4.83254	+	8.37020i	−0.663800	+	1.14973i	−0.979609	+	0.200912i	$0.935609\pi$
$54$		0			0
$55$	−3.33382	−	5.77435i	−0.449532	−	0.778613i
$56$	−17.2350	+	4.08478i	−2.30313	+	0.545851i
$57$		0			0
$58$	−4.91010	+	2.46595i	−0.644728	+	0.323795i
$59$	0.636054	−	1.47454i	0.0828072	−	0.191969i	−0.871782	−	0.489894i	$-0.837035\pi$
$59$	0.636054	−	1.47454i	0.0828072	−	0.191969i	0.954589	+	0.297926i	$0.0962947\pi$
$60$		0			0
$61$	0.0674875	+	1.15872i	0.00864089	+	0.148358i	0.999869	+	0.0161951i	$0.00515528\pi$
$61$	0.0674875	+	1.15872i	0.00864089	+	0.148358i	−0.991228	+	0.132163i	$0.957808\pi$
$62$	−1.63170	−	9.25383i	−0.207226	−	1.17524i
$63$		0			0
$64$	−0.847235	+	4.80491i	−0.105904	+	0.600613i
$65$	−2.98162	−	0.348502i	−0.369825	−	0.0432263i
$66$		0			0
$67$	1.71558	+	5.73045i	0.209592	+	0.700085i	0.996544	+	0.0830710i	$0.0264728\pi$
$67$	1.71558	+	5.73045i	0.209592	+	0.700085i	−0.786952	+	0.617014i	$0.788342\pi$
$68$	−12.3177	−	2.91935i	−1.49374	−	0.354024i
$69$		0			0
$70$	−4.43754	−	10.2874i	−0.530388	−	1.22958i
$71$	−2.74773	−	2.30562i	−0.326095	−	0.273626i	0.465011	−	0.885305i	$-0.346050\pi$
$71$	−2.74773	−	2.30562i	−0.326095	−	0.273626i	−0.791107	+	0.611678i	$0.790495\pi$
$72$		0			0
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.0145810	−	0.999894i	$-0.495359\pi$
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.987235	+	0.159270i	$0.0509141\pi$
$74$	14.9796	+	7.52304i	1.74134	+	0.874536i
$75$		0			0
$76$	−29.8185	+	3.48528i	−3.42041	+	0.399789i
$77$	0.878675	−	15.0863i	0.100134	−	1.71924i
$78$		0			0
$79$	−3.21730	−	3.41014i	−0.361975	−	0.383671i	0.520633	−	0.853780i	$-0.325696\pi$
$79$	−3.21730	−	3.41014i	−0.361975	−	0.383671i	−0.882608	+	0.470110i	$0.844214\pi$
$80$	7.60435			0.850192
$81$		0			0
$82$	10.5667			1.16690
$83$	10.2659	+	10.8812i	1.12683	+	1.19437i	0.978677	+	0.205406i	$0.0658516\pi$
$83$	10.2659	+	10.8812i	1.12683	+	1.19437i	0.148154	+	0.988964i	$0.452667\pi$
$84$		0			0
$85$	0.245199	−	4.20991i	0.0265956	−	0.456629i
$86$	−1.96748	+	0.229966i	−0.212159	+	0.0247978i
$87$		0			0
$88$	23.5034	+	11.8038i	2.50547	+	1.25829i
$89$	−3.17449	+	2.66371i	−0.336495	+	0.282353i	−0.795340	−	0.606164i	$-0.792708\pi$
$89$	−3.17449	+	2.66371i	−0.336495	+	0.282353i	0.458845	+	0.888516i	$0.348263\pi$
$90$		0			0
$91$	−5.21193	−	4.37333i	−0.546358	−	0.458449i
$92$	5.06091	+	11.7325i	0.527637	+	1.22320i
$93$		0			0
$94$	14.0460	+	3.32896i	1.44873	+	0.343356i
$95$	−2.86831	−	9.58083i	−0.294283	−	0.982973i
$96$		0			0
$97$	−12.5027	−	1.46135i	−1.26946	−	0.148378i	−0.545433	−	0.838154i	$-0.683635\pi$
$97$	−12.5027	−	1.46135i	−1.26946	−	0.148378i	−0.724023	+	0.689776i	$0.757709\pi$
$98$	1.37652	−	7.80666i	0.139050	−	0.788591i
$99$		0			0
$100$	−2.21491	−	12.5614i	−0.221491	−	1.25614i
$101$	−0.261942	−	4.49737i	−0.0260642	−	0.447505i	−0.985942	−	0.167087i	$-0.946564\pi$
$101$	−0.261942	−	4.49737i	−0.0260642	−	0.447505i	0.959878	−	0.280418i	$-0.0904732\pi$
$102$		0			0
$103$	5.52933	−	12.8184i	0.544821	−	1.26304i	−0.394152	−	0.919045i	$-0.628962\pi$
$103$	5.52933	−	12.8184i	0.544821	−	1.26304i	0.938973	−	0.343992i	$-0.111779\pi$
$104$	10.5817	−	5.31435i	1.03763	−	0.521115i
$105$		0			0
$106$	23.4648	−	5.56127i	2.27911	−	0.540158i
$107$	2.27719	+	3.94420i	0.220144	+	0.381301i	0.954852	−	0.297083i	$-0.0960139\pi$
$107$	2.27719	+	3.94420i	0.220144	+	0.381301i	−0.734708	+	0.678384i	$0.762681\pi$
$108$		0			0
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	−0.984772	−	0.173850i	$-0.944379\pi$
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	0.642944	+	0.765913i	$0.277713\pi$
$110$	−4.77129	+	15.9372i	−0.454925	+	1.51956i
$111$		0			0
$112$	14.3995	+	9.47070i	1.36062	+	0.894897i
$113$	−4.67557	−	6.28038i	−0.439840	−	0.590808i	0.525826	−	0.850592i	$-0.323756\pi$
$113$	−4.67557	−	6.28038i	−0.439840	−	0.590808i	−0.965667	+	0.259784i	$0.916349\pi$
$114$		0			0
$115$	−3.55629	+	2.33901i	−0.331626	+	0.218114i
$116$	8.74368	+	3.18244i	0.811830	+	0.295482i
$117$		0			0
$118$	−3.76510	+	1.37039i	−0.346606	+	0.126154i
$119$	5.70746	−	7.66645i	0.523202	−	0.702782i
$120$		0			0
$121$	−7.85014	+	8.32067i	−0.713649	+	0.756424i
$122$	1.98733	−	2.10644i	0.179924	−	0.190708i
$123$		0			0
$124$	−9.50247	+	12.7640i	−0.853347	+	1.14624i
$125$	10.6062	−	3.86035i	0.948650	−	0.345280i
$126$		0			0
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.731353	−	0.681999i	$-0.238889\pi$
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.121868	+	0.992546i	$0.461112\pi$
$128$	14.1395	−	9.29968i	1.24976	−	0.821983i
$129$		0			0
$130$	4.47269	+	6.00787i	0.392281	+	0.526925i
$131$	7.19028	+	4.72912i	0.628218	+	0.413185i	0.823304	−	0.567601i	$-0.192128\pi$
$131$	7.19028	+	4.72912i	0.628218	+	0.413185i	−0.195086	+	0.980786i	$0.562499\pi$
$132$		0			0
$133$	6.50087	−	21.7144i	0.563697	−	1.88288i
$134$	7.46238	−	12.9252i	0.644652	−	1.11657i
$135$		0			0
$136$	8.31720	+	14.4058i	0.713194	+	1.23529i
$137$	−1.03986	+	0.246452i	−0.0888413	+	0.0210558i	−0.274796	−	0.961503i	$-0.588610\pi$
$137$	−1.03986	+	0.246452i	−0.0888413	+	0.0210558i	0.185955	+	0.982558i	$0.440462\pi$
$138$		0			0
$139$	−6.65577	+	3.34265i	−0.564535	+	0.283520i	−0.708090	−	0.706122i	$-0.750443\pi$
$139$	−6.65577	+	3.34265i	−0.564535	+	0.283520i	0.143555	+	0.989642i	$0.454147\pi$
$140$	−7.51483	+	17.4213i	−0.635119	+	1.47237i
$141$		0			0
$142$	0.520368	+	8.93437i	0.0436683	+	0.749756i
$143$	1.75431	+	9.94920i	0.146703	+	0.831994i
$144$		0			0
$145$	−0.538257	+	3.05261i	−0.0446998	+	0.253505i
$146$	−27.6904	−	3.23654i	−2.29167	−	0.267858i
$147$		0			0
$148$	−8.14146	−	27.1944i	−0.669224	−	2.23536i
$149$	2.37562	+	0.563032i	0.194618	+	0.0461254i	0.326769	−	0.945104i	$-0.394040\pi$
$149$	2.37562	+	0.563032i	0.194618	+	0.0461254i	−0.132151	+	0.991230i	$0.542188\pi$
$150$		0			0
$151$	8.46731	+	19.6294i	0.689060	+	1.59742i	0.797501	+	0.603318i	$0.206155\pi$
$151$	8.46731	+	19.6294i	0.689060	+	1.59742i	−0.108440	+	0.994103i	$0.534586\pi$
$152$	30.2201	+	25.3577i	2.45117	+	2.05678i
$153$		0			0
$154$	−28.8836	+	24.2362i	−2.32751	+	1.95301i
$155$	−4.73715	−	2.37908i	−0.380497	−	0.191093i
$156$		0			0
$157$	6.41788	−	0.750143i	0.512203	−	0.0598679i	0.143934	−	0.989587i	$-0.454025\pi$
$157$	6.41788	−	0.750143i	0.512203	−	0.0598679i	0.368269	+	0.929719i	$0.379951\pi$
$158$	−0.680151	+	11.6777i	−0.0541099	+	0.929031i
$159$		0			0
$160$	−2.29416	−	2.43167i	−0.181369	−	0.192240i
$161$	−9.64722			−0.760307
$162$		0			0
$163$	−6.49040			−0.508367			−0.254184	−	0.967156i	$-0.581807\pi$
$163$	−6.49040			−0.508367			−0.254184	+	0.967156i	$0.581807\pi$
$164$	−12.2799	−	13.0159i	−0.958897	−	1.01637i
$165$		0			0
$166$	2.17026	−	37.2619i	0.168445	−	2.89208i
$167$	−3.87721	+	0.453181i	−0.300028	+	0.0350682i	−0.264775	−	0.964310i	$-0.585298\pi$
$167$	−3.87721	+	0.453181i	−0.300028	+	0.0350682i	−0.0352527	+	0.999378i	$0.511224\pi$
$168$		0			0
$169$	−7.55258	−	3.79305i	−0.580967	−	0.291773i
$170$	−8.06013	+	6.76325i	−0.618184	+	0.518718i
$171$		0			0
$172$	2.56973	+	2.15626i	0.195940	+	0.164413i
$173$	−6.46827	−	14.9951i	−0.491774	−	1.14006i	−0.965739	−	0.259516i	$-0.916437\pi$
$173$	−6.46827	−	14.9951i	−0.491774	−	1.14006i	0.473965	−	0.880544i	$-0.342822\pi$
$174$		0			0
$175$	9.37077	+	2.22091i	0.708364	+	0.167885i
$176$	−7.33979	−	24.5166i	−0.553258	−	1.84801i
$177$		0			0
$178$	10.2696	+	1.20034i	0.769737	+	0.0899694i
$179$	3.76729	−	21.3654i	0.281581	−	1.59692i	−0.435670	−	0.900107i	$-0.643488\pi$
$179$	3.76729	−	21.3654i	0.281581	−	1.59692i	0.717250	−	0.696816i	$-0.245401\pi$
$180$		0			0
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	−0.997963	−	0.0637968i	$-0.979679\pi$
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	0.915959	−	0.401273i	$-0.131432\pi$
$182$	0.987041	+	16.9468i	0.0731644	+	1.25618i
$183$		0			0
$184$	6.65026	−	15.4170i	0.490264	−	1.13656i
$185$	8.45061	−	4.24406i	0.621301	−	0.312029i
$186$		0			0
$187$	−13.8095	+	3.27292i	−1.00985	+	0.239339i
$188$	−12.2227	−	21.1703i	−0.891429	−	1.54400i
$189$		0			0
$190$	−12.4765	+	21.6099i	−0.905139	+	1.56775i
$191$	3.95814	−	13.2211i	0.286401	−	0.956646i	−0.686830	−	0.726818i	$-0.740998\pi$
$191$	3.95814	−	13.2211i	0.286401	−	0.956646i	0.973231	−	0.229828i	$-0.0738164\pi$
$192$		0			0
$193$	−3.15541	−	2.07534i	−0.227131	−	0.149387i	0.430843	−	0.902427i	$-0.358216\pi$
$193$	−3.15541	−	2.07534i	−0.227131	−	0.149387i	−0.657974	+	0.753040i	$0.728587\pi$
$194$	18.7551	+	25.1925i	1.34654	+	1.80871i
$195$		0			0
$196$	−11.2158	+	7.37675i	−0.801129	+	0.526911i
$197$	5.18414	+	1.88687i	0.369355	+	0.134434i	0.520027	−	0.854150i	$-0.325922\pi$
$197$	5.18414	+	1.88687i	0.369355	+	0.134434i	−0.150673	+	0.988584i	$0.548144\pi$
$198$		0			0
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.292148	−	0.956373i	$-0.405630\pi$
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.838543	+	0.544835i	$0.183408\pi$
$200$	−10.0089	+	13.4443i	−0.707736	+	0.950654i
$201$		0			0
$202$	−7.71350	+	8.17583i	−0.542720	+	0.575249i
$203$	−4.82105	+	5.11001i	−0.338371	+	0.358653i
$204$		0			0
$205$	3.55973	−	4.78155i	0.248622	−	0.333958i
$206$	−32.7307	+	11.9130i	−2.28046	+	0.830018i
$207$		0			0
$208$	−10.8271	−	3.94075i	−0.750725	−	0.273242i
$209$	−28.1203	+	18.4950i	−1.94512	+	1.27933i
$210$		0			0
$211$	11.5293	+	15.4866i	0.793712	+	1.06614i	0.996221	+	0.0868601i	$0.0276833\pi$
$211$	11.5293	+	15.4866i	0.793712	+	1.06614i	−0.202508	+	0.979281i	$0.564909\pi$
$212$	−34.1194	−	22.4407i	−2.34333	−	1.54123i
$213$		0			0
$214$	3.25906	−	10.8860i	0.222785	−	0.744153i
$215$	−0.558746	+	0.967777i	−0.0381062	+	0.0660018i
$216$		0			0
$217$	−6.00721	−	10.4048i	−0.407796	−	0.706323i
$218$	17.3286	−	4.10695i	1.17364	−	0.278158i
$219$		0			0
$220$	25.1761	−	12.6439i	1.69737	−	0.852452i
$221$	−2.53079	+	5.86702i	−0.170239	+	0.394659i
$222$		0			0
$223$	0.880079	+	15.1104i	0.0589345	+	1.01187i	0.890078	+	0.455808i	$0.150650\pi$
$223$	0.880079	+	15.1104i	0.0589345	+	1.01187i	−0.831144	+	0.556058i	$0.812313\pi$
$224$	−1.31572	−	7.46180i	−0.0879100	−	0.498562i
$225$		0			0
$226$	−3.39230	+	19.2387i	−0.225653	+	1.27974i
$227$	6.25901	+	0.731573i	0.415425	+	0.0485562i	0.321238	−	0.946998i	$-0.395901\pi$
$227$	6.25901	+	0.731573i	0.415425	+	0.0485562i	0.0941866	+	0.995555i	$0.469975\pi$
$228$		0			0
$229$	−2.67203	−	8.92519i	−0.176572	−	0.589793i	−0.999758	−	0.0220199i	$-0.992990\pi$
$229$	−2.67203	−	8.92519i	−0.176572	−	0.589793i	0.823185	−	0.567773i	$-0.192195\pi$
$230$	10.3340	+	2.44921i	0.681406	+	0.161496i
$231$		0			0
$232$	−4.84285	−	11.2270i	−0.317949	−	0.737088i
$233$	16.1221	+	13.5280i	1.05619	+	0.886251i	0.993731	−	0.111797i	$-0.0356606\pi$
$233$	16.1221	+	13.5280i	1.05619	+	0.886251i	0.0624612	+	0.998047i	$0.480105\pi$
$234$		0			0
$235$	6.23822	−	5.23449i	0.406937	−	0.341460i
$236$	6.06355	+	3.04523i	0.394703	+	0.198227i
$237$		0			0
$238$	−23.6857	+	2.76846i	−1.53532	+	0.179453i
$239$	−0.953580	+	16.3723i	−0.0616819	+	1.05904i	0.815462	+	0.578811i	$0.196483\pi$
$239$	−0.953580	+	16.3723i	−0.0616819	+	1.05904i	−0.877144	+	0.480227i	$0.840554\pi$
$240$		0			0
$241$	−1.13385	−	1.20181i	−0.0730377	−	0.0774155i	0.689824	−	0.723977i	$-0.257688\pi$
$241$	−1.13385	−	1.20181i	−0.0730377	−	0.0774155i	−0.762862	+	0.646562i	$0.776206\pi$
$242$	28.5417			1.83473
$243$		0			0
$244$	−4.90421			−0.313960
$245$	−3.06887	−	3.25281i	−0.196063	−	0.207814i
$246$		0			0
$247$	−0.881085	+	15.1277i	−0.0560621	+	0.962549i
$248$	20.7688	−	2.42752i	1.31882	−	0.154148i
$249$		0			0
$250$	−25.1660	−	12.6388i	−1.59164	−	0.799350i
$251$	16.6349	−	13.9583i	1.04998	−	0.881040i	0.0568910	−	0.998380i	$-0.481881\pi$
$251$	16.6349	−	13.9583i	1.04998	−	0.881040i	0.993092	+	0.117340i	$0.0374368\pi$
$252$		0			0
$253$	10.9736	+	9.20793i	0.689903	+	0.578898i
$254$	−10.1121	−	23.4424i	−0.634487	−	1.47091i
$255$		0			0
$256$	−31.5921	−	7.48747i	−1.97451	−	0.467967i
$257$	1.76523	+	5.89628i	0.110112	+	0.367800i	0.995229	−	0.0975692i	$-0.0311067\pi$
$257$	1.76523	+	5.89628i	0.110112	+	0.367800i	−0.885117	+	0.465369i	$0.845922\pi$
$258$		0			0
$259$	21.2876	+	2.48817i	1.32275	+	0.154607i
$260$	2.20255	−	12.4913i	0.136596	−	0.774677i
$261$		0			0
$262$	−3.72869	−	21.1464i	−0.230359	−	1.30643i
$263$	1.48444	+	25.4869i	0.0915345	+	1.57159i	0.661517	+	0.749930i	$0.269913\pi$
$263$	1.48444	+	25.4869i	0.0915345	+	1.57159i	−0.569983	+	0.821657i	$0.693050\pi$
$264$		0			0
$265$	5.38834	−	12.4916i	0.331003	−	0.767352i
$266$	−50.5390	+	25.3816i	−3.09874	+	1.55625i
$267$		0			0
$268$	−24.5933	+	5.82872i	−1.50228	+	0.356046i
$269$	−8.19176	−	14.1885i	−0.499460	−	0.865091i	0.500539	−	0.865714i	$-0.333135\pi$
$269$	−8.19176	−	14.1885i	−0.499460	−	0.865091i	−1.00000		0.000622889i	$0.999802\pi$
$270$		0			0
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	−0.0709627	−	0.997479i	$-0.522607\pi$
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	0.899323	−	0.437284i	$-0.144060\pi$
$272$	4.64215	−	15.5059i	0.281472	−	0.940182i
$273$		0			0
$274$	2.22773	+	1.46520i	0.134582	+	0.0885160i
$275$	−8.53935	−	11.4703i	−0.514942	−	0.691687i
$276$		0			0
$277$	19.1354	−	12.5855i	1.14973	−	0.756192i	0.176115	−	0.984370i	$-0.443647\pi$
$277$	19.1354	−	12.5855i	1.14973	−	0.756192i	0.973620	+	0.228177i	$0.0732766\pi$
$278$	17.4624	+	6.35580i	1.04733	+	0.381196i
$279$		0			0
$280$	23.4278	−	8.52704i	1.40008	−	0.509588i
$281$	−17.9072	+	24.0535i	−1.06825	+	1.43491i	−0.175439	+	0.984490i	$0.556134\pi$
$281$	−17.9072	+	24.0535i	−1.06825	+	1.43491i	−0.892815	+	0.450424i	$0.851273\pi$
$282$		0			0
$283$	−10.6483	+	11.2865i	−0.632975	+	0.670914i	−0.961887	−	0.273446i	$-0.911836\pi$
$283$	−10.6483	+	11.2865i	−0.632975	+	0.670914i	0.328912	+	0.944360i	$0.393318\pi$
$284$	10.4005	−	11.0239i	0.617155	−	0.654146i
$285$		0			0
$286$	15.0524	−	20.2189i	0.890068	−	1.19557i
$287$	12.6958	−	4.62088i	0.749407	−	0.272762i
$288$		0			0
$289$	7.54012	+	2.74438i	0.443536	+	0.161434i
$290$	6.46159	−	4.24985i	0.379438	−	0.249560i
$291$		0			0
$292$	28.1930	+	37.8698i	1.64987	+	2.21616i
$293$	−6.43251	−	4.23073i	−0.375791	−	0.247162i	0.347537	−	0.937666i	$-0.387018\pi$
$293$	−6.43251	−	4.23073i	−0.375791	−	0.247162i	−0.723328	+	0.690505i	$0.757388\pi$
$294$		0			0
$295$	−0.648280	+	2.16541i	−0.0377443	+	0.126075i
$296$	−18.6508	+	32.3042i	−1.08406	+	1.87764i
$297$		0			0
$298$	−3.04574	−	5.27538i	−0.176435	−	0.305595i
$299$	6.27559	−	1.48734i	0.362927	−	0.0860152i
$300$		0			0
$301$	−2.26333	+	1.13669i	−0.130456	+	0.0655177i
$302$	21.1264	−	48.9765i	1.21569	−	2.81828i
$303$		0			0
$304$	−2.23193	−	38.3208i	−0.128010	−	2.19785i
$305$	−0.283694	−	1.60891i	−0.0162443	−	0.0921258i
$306$		0			0
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	−0.847577	−	0.530673i	$-0.821939\pi$
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	0.977962	−	0.208781i	$-0.0669496\pi$
$308$	63.4202	+	7.41276i	3.61370	+	0.422381i
$309$		0			0
$310$	3.79334	+	12.6706i	0.215447	+	0.719644i
$311$	5.33273	+	1.26388i	0.302391	+	0.0716681i	0.379011	−	0.925392i	$-0.376264\pi$
$311$	5.33273	+	1.26388i	0.302391	+	0.0716681i	−0.0766191	+	0.997060i	$0.524413\pi$
$312$		0			0
$313$	9.57732	+	22.2027i	0.541342	+	1.25497i	0.941031	+	0.338321i	$0.109859\pi$
$313$	9.57732	+	22.2027i	0.541342	+	1.25497i	−0.399688	+	0.916651i	$0.630882\pi$
$314$	−12.3501	−	10.3630i	−0.696959	−	0.584818i
$315$		0			0
$316$	15.1749	−	12.7332i	0.853653	−	0.716300i
$317$	−9.24502	−	4.64302i	−0.519252	−	0.260778i	0.169815	−	0.985476i	$-0.445683\pi$
$317$	−9.24502	−	4.64302i	−0.519252	−	0.260778i	−0.689067	+	0.724698i	$0.741979\pi$
$318$		0			0
$319$	10.3612	−	1.21105i	0.580116	−	0.0678059i
$320$	0.399312	−	6.85592i	0.0223222	−	0.383258i
$321$		0			0
$322$	16.5181	+	17.5081i	0.920515	+	0.975689i
$323$	−21.2871			−1.18444
$324$		0			0
$325$	−6.43816			−0.357125
$326$	11.1129	+	11.7790i	0.615488	+	0.652379i
$327$		0			0
$328$	−1.36722	+	23.4742i	−0.0754920	+	1.29615i
$329$	18.3318	−	2.14268i	1.01066	−	0.118130i
$330$		0			0
$331$	−27.4917	−	13.8069i	−1.51108	−	0.758894i	−0.515873	−	0.856665i	$-0.672532\pi$
$331$	−27.4917	−	13.8069i	−1.51108	−	0.758894i	−0.995209	+	0.0977711i	$0.968829\pi$
$332$	−48.4207	+	40.6298i	−2.65743	+	2.22985i
$333$		0			0
$334$	7.46105	+	6.26056i	0.408250	+	0.342563i
$335$	−3.33486	−	7.73108i	−0.182203	−	0.422394i
$336$		0			0
$337$	−32.0522	−	7.59650i	−1.74599	−	0.413808i	−0.771141	−	0.636664i	$-0.780314\pi$
$337$	−32.0522	−	7.59650i	−1.74599	−	0.413808i	−0.974851	+	0.222856i	$0.928462\pi$
$338$	6.04784	+	20.2012i	0.328959	+	1.09880i
$339$		0			0
$340$	17.6978	+	2.06857i	0.959796	+	0.112184i
$341$	−3.09789	+	17.5690i	−0.167760	+	0.951414i
$342$		0			0
$343$	2.11774	+	12.0103i	0.114347	+	0.648496i
$344$	−0.256304	−	4.40056i	−0.0138190	−	0.237263i
$345$		0			0
$346$	−16.1387	+	37.4137i	−0.867621	+	2.01137i
$347$	23.1751	−	11.6390i	1.24410	−	0.624812i	0.299836	−	0.953991i	$-0.403068\pi$
$347$	23.1751	−	11.6390i	1.24410	−	0.624812i	0.944268	+	0.329178i	$0.106772\pi$
$348$		0			0
$349$	14.3802	−	3.40817i	0.769755	−	0.182435i	0.173069	−	0.984910i	$-0.444632\pi$
$349$	14.3802	−	3.40817i	0.769755	−	0.182435i	0.596686	+	0.802475i	$0.296484\pi$
$350$	−12.0141	−	20.8091i	−0.642182	−	1.11229i
$351$		0			0
$352$	−5.62541	+	9.74350i	−0.299836	+	0.519330i
$353$	1.98881	−	6.64309i	0.105854	−	0.353576i	−0.888609	−	0.458665i	$-0.848328\pi$
$353$	1.98881	−	6.64309i	0.105854	−	0.353576i	0.994463	+	0.105089i	$0.0335128\pi$
$354$		0			0
$355$	4.21820	+	2.77435i	0.223879	+	0.147247i
$356$	−10.4560	−	14.0448i	−0.554167	−	0.744375i
$357$		0			0
$358$	−45.2250	+	29.7450i	−2.39022	+	1.57207i
$359$	−28.2850	−	10.2949i	−1.49283	−	0.543344i	−0.538634	−	0.842540i	$-0.681060\pi$
$359$	−28.2850	−	10.2949i	−1.49283	−	0.543344i	−0.954192	+	0.299195i	$0.903282\pi$
$360$		0			0
$361$	−29.5849	+	10.7680i	−1.55710	+	0.566738i
$362$	−9.46619	+	12.7153i	−0.497532	+	0.668301i
$363$		0			0
$364$	19.7278	−	20.9102i	1.03402	−	1.09599i
$365$	−10.7929	+	11.4399i	−0.564929	+	0.598789i
$366$		0			0
$367$	−13.7405	+	18.4567i	−0.717247	+	0.963430i	0.282744	+	0.959195i	$0.408755\pi$
$367$	−13.7405	+	18.4567i	−0.717247	+	0.963430i	−0.999991	+	0.00423434i	$0.998652\pi$
$368$	−15.3522	+	5.58774i	−0.800288	+	0.291281i
$369$		0			0
$370$	−22.1715	−	8.06976i	−1.15264	−	0.419527i
$371$	25.7607	−	16.9431i	1.33743	−	0.879641i
$372$		0			0
$373$	−18.8164	−	25.2748i	−0.974276	−	1.30868i	−0.951079	−	0.308949i	$-0.900023\pi$
$373$	−18.8164	−	25.2748i	−0.974276	−	1.30868i	−0.0231970	−	0.999731i	$-0.507385\pi$
$374$	29.5846	+	19.4581i	1.52978	+	1.00615i
$375$		0			0
$376$	−9.21276	+	30.7728i	−0.475112	+	1.58698i
$377$	2.34830	−	4.06738i	0.120944	−	0.209481i
$378$		0			0
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	0.999867	−	0.0162889i	$-0.00518516\pi$
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	−0.514040	+	0.857766i	$0.671852\pi$
$380$	41.1180	−	9.74514i	2.10931	−	0.499915i
$381$		0			0
$382$	−30.7713	+	15.4539i	−1.57440	+	0.790692i
$383$	−11.8079	+	27.3739i	−0.603358	+	1.39874i	0.293302	+	0.956020i	$0.405246\pi$
$383$	−11.8079	+	27.3739i	−0.603358	+	1.39874i	−0.896659	+	0.442721i	$0.854013\pi$
$384$		0			0
$385$	1.23679	+	21.2349i	0.0630327	+	1.08223i
$386$	1.63631	+	9.27997i	0.0832859	+	0.472338i
$387$		0			0
$388$	9.23585	−	52.3791i	0.468879	−	2.65915i
$389$	5.79263	+	0.677061i	0.293698	+	0.0343283i	0.261666	−	0.965159i	$-0.415728\pi$
$389$	5.79263	+	0.677061i	0.293698	+	0.0343283i	0.0320318	+	0.999487i	$0.489802\pi$
$390$		0			0
$391$	2.59845	+	8.67943i	0.131409	+	0.438938i
$392$	17.1646	+	4.06808i	0.866942	+	0.205469i
$393$		0			0
$394$	−5.45197	−	12.6391i	−0.274666	−	0.636748i
$395$	5.05517	+	4.24179i	0.254353	+	0.213428i
$396$		0			0
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	−0.522710	−	0.852510i	$-0.675079\pi$
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	0.748791	+	0.662806i	$0.230635\pi$
$398$	−37.8463	−	19.0071i	−1.89706	−	0.952742i
$399$		0			0
$400$	16.1986	−	1.89335i	0.809931	−	0.0946674i
$401$	0.623901	−	10.7120i	0.0311561	−	0.534930i	−0.946234	−	0.323484i	$-0.895146\pi$
$401$	0.623901	−	10.7120i	0.0311561	−	0.534930i	0.977390	−	0.211446i	$-0.0678172\pi$
$402$		0			0
$403$	5.51187	+	5.84225i	0.274566	+	0.291023i
$404$	19.0349			0.947023
$405$		0			0
$406$	17.5285			0.869924
$407$	−21.8396	−	23.1486i	−1.08255	−	1.14743i
$408$		0			0
$409$	−0.193574	+	3.32353i	−0.00957161	+	0.164338i	0.990135	+	0.140117i	$0.0447478\pi$
$409$	−0.193574	+	3.32353i	−0.00957161	+	0.164338i	−0.999707	+	0.0242216i	$0.992289\pi$
$410$	−14.7727	+	1.72669i	−0.729573	+	0.0852749i
$411$		0			0
$412$	52.7115	+	26.4727i	2.59691	+	1.30422i
$413$	−3.92444	+	3.29300i	−0.193109	+	0.162038i
$414$		0			0
$415$	−16.1303	−	13.5349i	−0.791805	−	0.664403i
$416$	2.00629	+	4.65111i	0.0983665	+	0.228039i
$417$		0			0
$418$	81.7133	+	19.3664i	3.99673	+	0.947242i
$419$	0.820143	+	2.73947i	0.0400666	+	0.133832i	0.975683	−	0.219187i	$-0.0703404\pi$
$419$	0.820143	+	2.73947i	0.0400666	+	0.133832i	−0.935616	+	0.353019i	$0.885155\pi$
$420$		0			0
$421$	6.24383	+	0.729799i	0.304306	+	0.0355682i	0.266875	−	0.963731i	$-0.414009\pi$
$421$	6.24383	+	0.729799i	0.304306	+	0.0355682i	0.0374302	+	0.999299i	$0.488083\pi$
$422$	8.36498	−	47.4401i	0.407201	−	2.30935i
$423$		0			0
$424$	9.31841	+	52.8473i	0.452542	+	2.56649i
$425$	−0.525874	−	9.02891i	−0.0255086	−	0.437967i
$426$		0			0
$427$	1.46659	−	3.39993i	0.0709731	−	0.164534i
$428$	−17.1967	+	8.63649i	−0.831233	+	0.417461i
$429$		0			0
$430$	2.71305	−	0.643004i	0.130835	−	0.0310084i
$431$	8.66111	+	15.0015i	0.417191	+	0.722596i	0.995656	−	0.0931115i	$-0.0296813\pi$
$431$	8.66111	+	15.0015i	0.417191	+	0.722596i	−0.578465	+	0.815707i	$0.696348\pi$
$432$		0			0
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	−0.982191	−	0.187887i	$-0.939836\pi$
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	0.653810	+	0.756659i	$0.273170\pi$
$434$	−8.59739	+	28.7173i	−0.412688	+	1.37847i
$435$		0			0
$436$	−25.1969	−	16.5723i	−1.20671	−	0.793668i
$437$	12.8308	+	17.2348i	0.613781	+	0.824451i
$438$		0			0
$439$	31.1535	−	20.4900i	1.48688	−	0.977934i	0.492696	−	0.870202i	$-0.336012\pi$
$439$	31.1535	−	20.4900i	1.48688	−	0.977934i	0.994180	−	0.107732i	$-0.0343588\pi$
$440$	−34.7876	−	12.6617i	−1.65843	−	0.603621i
$441$		0			0
$442$	14.9809	−	5.45261i	0.712570	−	0.259354i
$443$	2.66634	−	3.58151i	0.126682	−	0.170163i	−0.734257	−	0.678871i	$-0.762469\pi$
$443$	2.66634	−	3.58151i	0.126682	−	0.170163i	0.860939	+	0.508708i	$0.169877\pi$
$444$		0			0
$445$	4.00280	−	4.24272i	0.189751	−	0.201124i
$446$	25.9160	−	27.4693i	1.22716	−	1.30071i
$447$		0			0
$448$	9.29471	−	12.4850i	0.439134	−	0.589859i
$449$	3.44438	−	1.25365i	0.162550	−	0.0591635i	−0.259463	−	0.965753i	$-0.583546\pi$
$449$	3.44438	−	1.25365i	0.162550	−	0.0591635i	0.422014	+	0.906589i	$0.361323\pi$
$450$		0			0
$451$	−18.8517	−	6.86146i	−0.887693	−	0.323094i
$452$	27.6402	−	18.1793i	1.30009	−	0.855080i
$453$		0			0
$454$	−9.38905	−	12.6117i	−0.440650	−	0.591896i
$455$	8.00114	+	5.26243i	0.375099	+	0.246707i
$456$		0			0
$457$	5.26887	−	17.5993i	0.246467	−	0.823259i	−0.741813	−	0.670607i	$-0.766034\pi$
$457$	5.26887	−	17.5993i	0.246467	−	0.823259i	0.988280	−	0.152651i	$-0.0487812\pi$
$458$	−11.6227	+	20.1311i	−0.543092	+	0.940664i
$459$		0			0
$460$	−8.99256	−	15.5756i	−0.419280	−	0.726215i
$461$	11.7380	−	2.78196i	0.546694	−	0.129569i	0.0520176	−	0.998646i	$-0.483435\pi$
$461$	11.7380	−	2.78196i	0.546694	−	0.129569i	0.494676	+	0.869077i	$0.335287\pi$
$462$		0			0
$463$	2.46047	−	1.23569i	0.114348	−	0.0574275i	−0.390706	−	0.920516i	$-0.627769\pi$
$463$	2.46047	−	1.23569i	0.114348	−	0.0574275i	0.505053	+	0.863088i	$0.331473\pi$
$464$	−4.71226	+	10.9242i	−0.218761	+	0.507145i
$465$		0			0
$466$	−3.05322	−	52.4217i	−0.141438	−	2.42839i
$467$	−5.46587	−	30.9985i	−0.252930	−	1.43444i	−0.801330	−	0.598223i	$-0.795874\pi$
$467$	−5.46587	−	30.9985i	−0.252930	−	1.43444i	0.548399	−	0.836216i	$-0.315237\pi$
$468$		0			0
$469$	3.31368	−	18.7928i	0.153011	−	0.867771i
$470$	−20.1809	−	2.35881i	−0.930874	−	0.108804i
$471$		0			0
$472$	−2.55718	−	8.54159i	−0.117704	−	0.393158i
$473$	3.65944	+	0.867304i	0.168261	+	0.0398787i
$474$		0			0
$475$	−8.49548	−	19.6947i	−0.389799	−	0.903656i
$476$	30.9360	+	25.9584i	1.41795	+	1.18980i
$477$		0			0
$478$	31.3458	−	26.3023i	1.43372	−	1.20304i
$479$	−2.49117	−	1.25111i	−0.113825	−	0.0571648i	0.390976	−	0.920401i	$-0.372138\pi$
$479$	−2.49117	−	1.25111i	−0.113825	−	0.0571648i	−0.504800	+	0.863236i	$0.668434\pi$
$480$		0			0
$481$	−14.2314	+	1.66341i	−0.648895	+	0.0758450i
$482$	−0.239701	+	4.11551i	−0.0109181	+	0.187456i
$483$		0			0
$484$	−33.1691	−	35.1572i	−1.50769	−	1.59806i
$485$	17.7181			0.804538
$486$		0			0
$487$	−31.6987			−1.43640			−0.718202	−	0.695835i	$-0.755035\pi$
$487$	−31.6987			−1.43640			−0.718202	+	0.695835i	$0.755035\pi$
$488$	4.42238	+	4.68745i	0.200192	+	0.212191i
$489$		0			0
$490$	−0.648772	+	11.1390i	−0.0293085	+	0.503208i
$491$	−34.9560	+	4.08577i	−1.57754	+	0.184388i	−0.859324	−	0.511431i	$-0.829116\pi$
$491$	−34.9560	+	4.08577i	−1.57754	+	0.184388i	−0.718217	+	0.695819i	$0.755041\pi$
$492$		0			0
$493$	5.89592	+	2.96104i	0.265539	+	0.133359i
$494$	28.9628	−	24.3027i	1.30310	−	1.09343i
$495$		0			0
$496$	−15.5862	−	13.0783i	−0.699839	−	0.587235i
$497$	4.53226	+	10.5070i	0.203300	+	0.471302i
$498$		0			0
$499$	−7.77433	−	1.84255i	−0.348027	−	0.0824838i	0.0528848	−	0.998601i	$-0.483158\pi$
$499$	−7.77433	−	1.84255i	−0.348027	−	0.0824838i	−0.400912	+	0.916117i	$0.631307\pi$
$500$	13.6778	+	45.6870i	0.611689	+	2.04318i
$501$		0			0
$502$	−53.8144	−	6.29000i	−2.40185	−	0.280736i
$503$	2.70376	−	15.3338i	0.120555	−	0.683700i	−0.863294	−	0.504701i	$-0.831603\pi$
$503$	2.70376	−	15.3338i	0.120555	−	0.683700i	0.983849	−	0.178999i	$-0.0572860\pi$
$504$		0			0
$505$	1.10111	+	6.24473i	0.0489989	+	0.277887i
$506$	−2.07819	−	35.6812i	−0.0923868	−	1.58622i
$507$		0			0
$508$	−17.1244	+	39.6989i	−0.759774	+	1.76136i
$509$	15.4415	−	7.75504i	0.684435	−	0.343736i	−0.0723693	−	0.997378i	$-0.523056\pi$
$509$	15.4415	−	7.75504i	0.684435	−	0.343736i	0.756804	+	0.653642i	$0.226760\pi$
$510$		0			0
$511$	−34.6849	+	8.22048i	−1.53437	+	0.363653i
$512$	23.5802	+	40.8420i	1.04211	+	1.80498i
$513$		0			0
$514$	7.67834	−	13.2993i	0.338677	−	0.586606i
$515$	−5.63561	+	18.8243i	−0.248335	+	0.829496i
$516$		0			0
$517$	−22.8973	−	15.0598i	−1.00702	−	0.662329i
$518$	−31.9333	−	42.8939i	−1.40307	−	1.88465i
$519$		0			0
$520$	−13.9253	+	9.15885i	−0.610667	+	0.401642i
$521$	33.0219	+	12.0190i	1.44672	+	0.526562i	0.941672	−	0.336531i	$-0.109254\pi$
$521$	33.0219	+	12.0190i	1.44672	+	0.526562i	0.505045	+	0.863093i	$0.331476\pi$
$522$		0			0
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	−0.285616	−	0.958344i	$-0.592198\pi$
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	0.397218	+	0.917724i	$0.369976\pi$
$524$	−21.7146	+	29.1678i	−0.948607	+	1.27420i
$525$		0			0
$526$	43.7128	−	46.3328i	1.90597	−	2.02021i
$527$	−7.74298	+	8.20708i	−0.337290	+	0.357506i
$528$		0			0
$529$	−8.27369	+	11.1135i	−0.359726	+	0.483195i
$530$	−31.8961	+	11.6092i	−1.38548	+	0.504273i
$531$		0			0
$532$	89.9974	+	32.7564i	3.90188	+	1.42017i
$533$	−7.54627	+	4.96326i	−0.326865	+	0.214983i
$534$		0			0
$535$	−3.82812	−	5.14206i	−0.165504	−	0.222311i
$536$	27.7482	+	18.2503i	1.19854	+	0.788291i
$537$		0			0
$538$	−11.7239	+	39.1605i	−0.505452	+	1.68833i
$539$	−7.52504	+	13.0337i	−0.324126	+	0.561403i
$540$		0			0
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	0.873772	+	0.486336i	$0.161667\pi$
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	−0.0157071	+	0.999877i	$0.505000\pi$
$542$	−66.2135	+	15.6929i	−2.84412	+	0.674068i
$543$		0			0
$544$	−6.35886	+	3.19354i	−0.272634	+	0.136922i
$545$	3.97924	−	9.22493i	0.170452	−	0.395152i
$546$		0			0
$547$	0.540346	+	9.27738i	0.0231035	+	0.396672i	0.989960	+	0.141350i	$0.0451444\pi$
$547$	0.540346	+	9.27738i	0.0231035	+	0.396672i	−0.966856	+	0.255322i	$0.917819\pi$
$548$	−0.784096	−	4.44683i	−0.0334949	−	0.189959i
$549$		0			0
$550$	−6.19562	+	35.1371i	−0.264182	+	1.49825i
$551$	15.5411	+	1.81649i	0.662071	+	0.0773850i
$552$		0			0
$553$	4.28954	+	14.3281i	0.182410	+	0.609292i
$554$	−55.6045	−	13.1785i	−2.36241	−	0.559901i
$555$		0			0
$556$	−12.4646	−	28.8962i	−0.528617	−	1.22547i
$557$	−28.8895	−	24.2411i	−1.22409	−	1.02713i	−0.998601	−	0.0528835i	$-0.983159\pi$
$557$	−28.8895	−	24.2411i	−1.22409	−	1.02713i	−0.225485	−	0.974247i	$-0.572397\pi$
$558$		0			0
$559$	1.29707	−	1.08837i	0.0548602	−	0.0460332i
$560$	−21.6787	−	10.8875i	−0.916093	−	0.460079i
$561$		0			0
$562$	74.3141	−	8.68607i	3.13475	−	0.366400i
$563$	−2.31955	+	39.8251i	−0.0977572	+	1.67843i	0.491806	+	0.870705i	$0.336337\pi$
$563$	−2.31955	+	39.8251i	−0.0977572	+	1.67843i	−0.589564	+	0.807722i	$0.700700\pi$
$564$		0			0
$565$	7.56291	+	8.01622i	0.318174	+	0.337245i
$566$	38.7153			1.62732
$567$		0			0
$568$	−19.9153			−0.835626
$569$	21.4166	+	22.7003i	0.897831	+	0.951646i	0.999066	−	0.0432171i	$-0.0137607\pi$
$569$	21.4166	+	22.7003i	0.897831	+	0.951646i	−0.101234	+	0.994863i	$0.532279\pi$
$570$		0			0
$571$	1.25067	−	21.4732i	0.0523390	−	0.898627i	−0.865311	−	0.501236i	$-0.832879\pi$
$571$	1.25067	−	21.4732i	0.0523390	−	0.898627i	0.917650	−	0.397390i	$-0.130084\pi$
$572$	−42.3982	+	4.95563i	−1.77276	+	0.207205i
$573$		0			0
$574$	−30.1239	−	15.1288i	−1.25735	−	0.631464i
$575$	−6.99316	+	5.86796i	−0.291635	+	0.244711i
$576$		0			0
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	0.664582	−	0.747215i	$-0.268610\pi$
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	−0.620460	+	0.784238i	$0.713054\pi$
$578$	−7.92966	−	18.3830i	−0.329831	−	0.764633i
$579$		0			0
$580$	−12.7441	−	3.02040i	−0.529170	−	0.125415i
$581$	−13.6873	−	45.7187i	−0.567844	−	1.89673i
$582$		0			0
$583$	−45.4740	−	5.31515i	−1.88334	−	0.220131i
$584$	10.7729	−	61.0961i	0.445785	−	2.52817i
$585$		0			0
$586$	3.33572	+	18.9178i	0.137797	+	0.781488i
$587$	−0.466073	−	8.00217i	−0.0192369	−	0.330285i	−0.994173	−	0.107799i	$-0.965620\pi$
$587$	−0.466073	−	8.00217i	−0.0192369	−	0.330285i	0.974936	−	0.222486i	$-0.0714172\pi$
$588$		0			0
$589$	−10.5986	+	24.5703i	−0.436707	+	1.01240i
$590$	5.03985	−	2.53111i	0.207487	−	0.104204i
$591$		0			0
$592$	35.3175	−	8.37039i	1.45154	−	0.344021i
$593$	10.7066	+	18.5444i	0.439668	+	0.761527i	0.997664	−	0.0683166i	$-0.0217628\pi$
$593$	10.7066	+	18.5444i	0.439668	+	0.761527i	−0.557996	+	0.829844i	$0.688429\pi$
$594$		0			0
$595$	−6.72652	+	11.6507i	−0.275761	+	0.477631i
$596$	−2.95859	+	9.88237i	−0.121188	+	0.404798i
$597$		0			0
$598$	−13.4444	−	8.84252i	−0.549782	−	0.361598i
$599$	13.8938	+	18.6626i	0.567684	+	0.762531i	0.989560	−	0.144122i	$-0.0460357\pi$
$599$	13.8938	+	18.6626i	0.567684	+	0.762531i	−0.421876	+	0.906653i	$0.638628\pi$
$600$		0			0
$601$	26.3770	−	17.3485i	1.07594	−	0.707658i	0.117537	−	0.993069i	$-0.462500\pi$
$601$	26.3770	−	17.3485i	1.07594	−	0.707658i	0.958405	+	0.285410i	$0.0921298\pi$
$602$	5.93821	+	2.16133i	0.242023	+	0.0880893i
$603$		0			0
$604$	−84.8800	+	30.8938i	−3.45372	+	1.25705i
$605$	9.61519	−	12.9154i	0.390913	−	0.525087i
$606$		0			0
$607$	3.23033	−	3.42395i	0.131115	−	0.138974i	−0.658489	−	0.752590i	$-0.728804\pi$
$607$	3.23033	−	3.42395i	0.131115	−	0.138974i	0.789605	+	0.613616i	$0.210286\pi$
$608$	−11.5806	+	12.2747i	−0.469656	+	0.497806i
$609$		0			0
$610$	−2.43416	+	3.26965i	−0.0985563	+	0.132384i
$611$	−11.5946	+	4.22010i	−0.469069	+	0.170727i
$612$		0			0
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.991082	−	0.133255i	$-0.0425429\pi$
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.673558	+	0.739134i	$0.264765\pi$
$614$	−27.4251	+	18.0378i	−1.10679	+	0.727946i
$615$		0			0
$616$	−50.1041	−	67.3015i	−2.01875	−	2.71166i
$617$	−14.8817	−	9.78784i	−0.599114	−	0.394044i	0.213417	−	0.976961i	$-0.431541\pi$
$617$	−14.8817	−	9.78784i	−0.599114	−	0.394044i	−0.812531	+	0.582918i	$0.801911\pi$
$618$		0			0
$619$	−1.60750	+	5.36943i	−0.0646109	+	0.215816i	−0.984198	−	0.177070i	$-0.943338\pi$
$619$	−1.60750	+	5.36943i	−0.0646109	+	0.215816i	0.919587	+	0.392886i	$0.128523\pi$
$620$	11.1991	−	19.3975i	0.449768	−	0.779021i
$621$		0			0
$622$	−6.83702	−	11.8421i	−0.274139	−	0.474823i
$623$	12.8637	−	3.04874i	0.515372	−	0.122145i
$624$		0			0
$625$	−0.708810	+	0.355978i	−0.0283524	+	0.0142391i
$626$	23.8959	−	55.3970i	0.955074	−	2.21411i
$627$		0			0
$628$	1.58747	+	27.2558i	0.0633470	+	1.08763i
$629$	−3.49521	−	19.8223i	−0.139363	−	0.790367i
$630$		0			0
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	0.874622	+	0.484806i	$0.161110\pi$
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	−0.987689	+	0.156431i	$0.950001\pi$
$632$	−25.8544	−	3.02195i	−1.02843	−	0.120207i
$633$		0			0
$634$	7.40308	+	24.7280i	0.294014	+	0.982075i
$635$	−14.0145	−	3.32150i	−0.556149	−	0.131810i
$636$		0			0
$637$	2.68379	+	6.22172i	0.106336	+	0.246514i
$638$	−19.9384	−	16.7303i	−0.789369	−	0.662360i
$639$		0			0
$640$	−18.2480	+	15.3119i	−0.721314	+	0.605255i
$641$	−20.8476	−	10.4700i	−0.823429	−	0.413541i	−0.0133847	−	0.999910i	$-0.504261\pi$
$641$	−20.8476	−	10.4700i	−0.823429	−	0.413541i	−0.810044	+	0.586369i	$0.800557\pi$
$642$		0			0
$643$	14.4953	−	1.69426i	0.571638	−	0.0668149i	0.174637	−	0.984633i	$-0.444125\pi$
$643$	14.4953	−	1.69426i	0.571638	−	0.0668149i	0.397002	+	0.917818i	$0.370051\pi$
$644$	2.37012	−	40.6933i	0.0933957	−	1.60354i
$645$		0			0
$646$	36.4479	+	38.6325i	1.43402	+	1.51998i
$647$	−1.33592			−0.0525205			−0.0262602	−	0.999655i	$-0.508360\pi$
$647$	−1.33592			−0.0525205			−0.0262602	+	0.999655i	$0.508360\pi$
$648$		0			0
$649$	7.60705			0.298603
$650$	11.0235	+	11.6842i	0.432377	+	0.458292i
$651$		0			0
$652$	1.59455	−	27.3774i	0.0624475	−	1.07218i
$653$	16.3676	−	1.91310i	0.640514	−	0.0748654i	0.210365	−	0.977623i	$-0.432535\pi$
$653$	16.3676	−	1.91310i	0.640514	−	0.0748654i	0.430150	+	0.902758i	$0.358461\pi$
$654$		0			0
$655$	−10.8251	−	5.43657i	−0.422972	−	0.212424i
$656$	17.5271	−	14.7069i	0.684316	−	0.574210i
$657$		0			0
$658$	−35.2765	−	29.6005i	−1.37522	−	1.15395i
$659$	17.8283	+	41.3307i	0.694493	+	1.61002i	0.788929	+	0.614484i	$0.210636\pi$
$659$	17.8283	+	41.3307i	0.694493	+	1.61002i	−0.0944361	+	0.995531i	$0.530105\pi$
$660$		0			0
$661$	24.2010	+	5.73574i	0.941310	+	0.223094i	0.672499	−	0.740098i	$-0.265221\pi$
$661$	24.2010	+	5.73574i	0.941310	+	0.223094i	0.268811	+	0.963193i	$0.413369\pi$
$662$	22.0144	+	73.5332i	0.855614	+	2.85795i
$663$		0			0
$664$	82.4975	+	9.64257i	3.20152	+	0.374204i
$665$	−5.54020	+	31.4200i	−0.214840	+	1.21842i
$666$		0			0
$667$	−1.15641	−	6.55832i	−0.0447764	−	0.253939i
$668$	−0.959034	−	16.4660i	−0.0371061	−	0.637087i
$669$		0			0
$670$	−8.32066	+	19.2895i	−0.321455	+	0.745217i
$671$	−4.91333	+	2.46757i	−0.189677	+	0.0952594i
$672$		0			0
$673$	1.92706	−	0.456722i	0.0742827	−	0.0176053i	−0.193306	−	0.981138i	$-0.561921\pi$
$673$	1.92706	−	0.456722i	0.0742827	−	0.0176053i	0.267589	+	0.963533i	$0.413773\pi$
$674$	41.0936	+	71.1762i	1.58287	+	2.74161i
$675$		0			0
$676$	17.8551	−	30.9260i	0.686735	−	1.18946i
$677$	8.17155	−	27.2949i	0.314058	−	1.04903i	−0.644613	−	0.764509i	$-0.722981\pi$
$677$	8.17155	−	27.2949i	0.314058	−	1.04903i	0.958671	−	0.284518i	$-0.0918335\pi$
$678$		0			0
$679$	33.5508	+	22.0667i	1.28756	+	0.846842i
$680$	−13.9818	−	18.7809i	−0.536179	−	0.720214i
$681$		0			0
$682$	37.1891	−	24.4596i	1.42404	−	0.936608i
$683$	−27.6811	−	10.0751i	−1.05919	−	0.385512i	−0.247064	−	0.968999i	$-0.579466\pi$
$683$	−27.6811	−	10.0751i	−1.05919	−	0.385512i	−0.812123	+	0.583487i	$0.801688\pi$
$684$		0			0
$685$	1.41350	−	0.514472i	0.0540071	−	0.0196570i
$686$	18.1707	−	24.4075i	0.693762	−	0.931884i
$687$		0			0
$688$	−2.94340	+	3.11982i	−0.112216	+	0.118942i
$689$	−14.1454	+	14.9932i	−0.538895	+	0.571196i
$690$		0			0
$691$	29.0246	−	38.9868i	1.10415	−	1.48313i	0.246320	−	0.969189i	$-0.420779\pi$
$691$	29.0246	−	38.9868i	1.10415	−	1.48313i	0.857827	−	0.513938i	$-0.171814\pi$
$692$	64.8408	−	23.6001i	2.46488	−	0.897141i
$693$		0			0
$694$	−60.8034	−	22.1306i	−2.30807	−	0.840067i
$695$	8.75884	−	5.76078i	0.332242	−	0.218519i
$696$		0			0
$697$	−7.57688	−	10.1775i	−0.286995	−	0.385501i
$698$	−30.8072	−	20.2622i	−1.16607	−	0.766936i
$699$		0			0
$700$	−11.6703	+	38.9816i	−0.441097	+	1.47337i
$701$	−3.03784	+	5.26170i	−0.114738	+	0.198732i	−0.917675	−	0.397332i	$-0.869936\pi$
$701$	−3.03784	+	5.26170i	−0.114738	+	0.198732i	0.802937	+	0.596064i	$0.203269\pi$
$702$		0			0
$703$	−23.8675	−	41.3397i	−0.900179	−	1.55916i
$704$	−22.4891	+	5.33001i	−0.847589	+	0.200882i
$705$		0			0
$706$	−15.4614	+	7.76500i	−0.581897	+	0.292240i
$707$	−5.69232	+	13.1963i	−0.214082	+	0.496297i
$708$		0			0
$709$	1.26191	+	21.6661i	0.0473919	+	0.813688i	0.935341	+	0.353747i	$0.115092\pi$
$709$	1.26191	+	21.6661i	0.0473919	+	0.813688i	−0.887949	+	0.459941i	$0.847871\pi$
$710$	−2.18745	−	12.4056i	−0.0820934	−	0.465575i
$711$		0			0
$712$	−3.99536	+	22.6588i	−0.149733	+	0.849175i
$713$	11.3118	+	1.32216i	0.423632	+	0.0495155i
$714$		0			0
$715$	−4.07839	−	13.6228i	−0.152523	−	0.509462i
$716$	89.1966	+	21.1400i	3.33343	+	0.790038i
$717$		0			0
$718$	29.7463	+	68.9597i	1.11012	+	2.57355i
$719$	11.8323	+	9.92847i	0.441270	+	0.370269i	0.836184	−	0.548449i	$-0.184781\pi$
$719$	11.8323	+	9.92847i	0.441270	+	0.370269i	−0.394915	+	0.918718i	$0.629226\pi$
$720$		0			0
$721$	−34.1158	+	28.6266i	−1.27054	+	1.06611i
$722$	70.1977	+	35.2546i	2.61249	+	1.31204i
$723$		0			0
$724$	26.6634	−	3.11651i	0.990938	−	0.115824i
$725$	−0.386539	+	6.63661i	−0.0143557	+	0.246478i
$726$		0			0
$727$	17.6753	+	18.7348i	0.655542	+	0.694833i	0.966812	−	0.255488i	$-0.0822361\pi$
$727$	17.6753	+	18.7348i	0.655542	+	0.694833i	−0.311271	+	0.950321i	$0.600755\pi$
$728$	−37.7756			−1.40006
$729$		0			0
$730$	39.2412			1.45238
$731$	1.63228	+	1.73012i	0.0603721	+	0.0639907i
$732$		0			0
$733$	−1.69715	+	29.1389i	−0.0626857	+	1.07627i	0.809507	+	0.587110i	$0.199734\pi$
$733$	−1.69715	+	29.1389i	−0.0626857	+	1.07627i	−0.872193	+	0.489162i	$0.837303\pi$
$734$	57.0224	−	6.66496i	2.10473	−	0.246008i
$735$		0			0
$736$	6.41842	+	3.22345i	0.236586	+	0.118818i
$737$	−21.7063	+	18.2138i	−0.799563	+	0.670913i
$738$		0			0
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	0.883650	−	0.468148i	$-0.155079\pi$
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	−0.307592	+	0.951518i	$0.599523\pi$
$740$	15.8259	+	36.6886i	0.581772	+	1.34870i
$741$		0			0
$742$	−74.8566	−	17.7413i	−2.74807	−	0.651305i
$743$	−6.73922	−	22.5106i	−0.247238	−	0.825832i	−0.988052	−	0.154122i	$-0.950745\pi$
$743$	−6.73922	−	22.5106i	−0.247238	−	0.825832i	0.740814	−	0.671710i	$-0.234440\pi$
$744$		0			0
$745$	−3.41322	−	0.398948i	−0.125051	−	0.0146163i
$746$	−13.6520	+	77.4244i	−0.499836	+	2.83471i
$747$		0			0
$748$	−10.4129	−	59.0546i	−0.380734	−	2.15925i
$749$	−0.844797	−	14.5046i	−0.0308682	−	0.529987i
$750$		0			0
$751$	13.9011	−	32.2264i	0.507259	−	1.17596i	−0.451637	−	0.892202i	$-0.649160\pi$
$751$	13.9011	−	32.2264i	0.507259	−	1.17596i	0.958896	−	0.283757i	$-0.0915810\pi$
$752$	27.9314	−	14.0277i	1.01855	−	0.511537i
$753$		0			0
$754$	−11.4024	+	2.70242i	−0.415251	+	0.0984163i
$755$	−15.0453	−	26.0592i	−0.547554	−	0.948391i
$756$		0			0
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	0.0476764	+	0.998863i	$0.484818\pi$
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	−0.888879	+	0.458142i	$0.848515\pi$
$758$	13.5361	−	45.2139i	0.491655	−	1.64224i
$759$		0			0
$760$	−46.3926	−	30.5129i	−1.68284	−	1.10682i
$761$	−4.23035	−	5.68235i	−0.153350	−	0.205985i	0.718809	−	0.695208i	$-0.244688\pi$
$761$	−4.23035	−	5.68235i	−0.153350	−	0.205985i	−0.872159	+	0.489223i	$0.837280\pi$
$762$		0			0
$763$	19.0241	−	12.5123i	0.688717	−	0.452976i
$764$	54.7961	+	19.9441i	1.98245	+	0.721554i
$765$		0			0
$766$	69.8968	−	25.4404i	2.52547	−	0.919198i
$767$	2.04519	−	2.74716i	0.0738474	−	0.0991943i
$768$		0			0
$769$	29.7305	−	31.5125i	1.07211	−	1.13637i	0.0819197	−	0.996639i	$-0.473895\pi$
$769$	29.7305	−	31.5125i	1.07211	−	1.13637i	0.990190	−	0.139731i	$-0.0446236\pi$
$770$	36.4202	−	38.6031i	1.31249	−	1.39116i
$771$		0			0
$772$	9.52931	−	12.8001i	0.342967	−	0.460685i
$773$	−33.8164	+	12.3082i	−1.21629	+	0.442694i	−0.868881	−	0.495020i	$-0.835161\pi$
$773$	−33.8164	+	12.3082i	−1.21629	+	0.442694i	−0.347409	+	0.937714i	$0.612938\pi$
$774$		0			0
$775$	−10.6833	−	3.88841i	−0.383756	−	0.139676i
$776$	−58.3924	+	38.4053i	−2.09617	+	1.37867i
$777$		0			0
$778$	−8.68943	−	11.6719i	−0.311531	−	0.418459i
$779$	−25.1406	−	16.5352i	−0.900755	−	0.592436i
$780$		0			0
$781$	4.87314	−	16.2774i	0.174375	−	0.582452i
$782$	11.3026	−	19.5768i	0.404182	−	0.700063i
$783$		0			0
$784$	−8.58220	−	14.8648i	−0.306507	−	0.530886i
$785$	−8.84990	+	2.09747i	−0.315867	+	0.0748618i
$786$		0			0
$787$	18.7666	−	9.42494i	0.668957	−	0.335963i	−0.0816980	−	0.996657i	$-0.526034\pi$
$787$	18.7666	−	9.42494i	0.668957	−	0.335963i	0.750655	+	0.660694i	$0.229738\pi$
$788$	−9.23273	+	21.4039i	−0.328902	+	0.762481i
$789$		0			0
$790$	−0.957355	−	16.4371i	−0.0340611	−	0.584807i
$791$	4.33738	+	24.5985i	0.154219	+	0.874622i
$792$		0			0
$793$	−0.429848	+	2.43779i	−0.0152643	+	0.0865683i
$794$	−14.5726	−	1.70330i	−0.517163	−	0.0604477i
$795$		0			0
$796$	20.5696	+	68.7072i	0.729070	+	2.43526i
$797$	41.0669	+	9.73304i	1.45467	+	0.344762i	0.880527	−	0.473996i	$-0.157189\pi$
$797$	41.0669	+	9.73304i	1.45467	+	0.344762i	0.574139	+	0.818758i	$0.305337\pi$
$798$		0			0
$799$	−6.86535	−	15.9157i	−0.242879	−	0.563056i
$800$	−5.49242	−	4.60868i	−0.194186	−	0.162942i
$801$		0			0
$802$	−20.5087	+	17.2089i	−0.724188	+	0.607666i
$803$	47.2998	+	23.7549i	1.66917	+	0.838291i
$804$		0			0
$805$	13.4872	−	1.57643i	0.475363	−	0.0555619i
$806$	1.16523	−	20.0063i	0.0410436	−	0.704692i
$807$		0			0
$808$	−17.1648	−	18.1936i	−0.603855	−	0.640048i
$809$	−15.1427			−0.532390			−0.266195	−	0.963919i	$-0.585767\pi$
$809$	−15.1427			−0.532390			−0.266195	+	0.963919i	$0.585767\pi$
$810$		0			0
$811$	30.4862			1.07051			0.535257	−	0.844689i	$-0.320215\pi$
$811$	30.4862			1.07051			0.535257	+	0.844689i	$0.320215\pi$
$812$	−20.3703	−	21.5913i	−0.714858	−	0.757706i
$813$		0			0
$814$	−4.61698	+	79.2704i	−0.161825	+	2.77843i
$815$	9.07386	−	1.06058i	0.317844	−	0.0371506i
$816$		0			0
$817$	5.04094	+	2.53165i	0.176360	+	0.0885714i
$818$	6.36311	−	5.33928i	0.222481	−	0.186684i
$819$		0			0
$820$	19.2947	+	16.1902i	0.673800	+	0.565386i
$821$	17.6031	+	40.8085i	0.614352	+	1.42423i	0.886844	+	0.462070i	$0.152893\pi$
$821$	17.6031	+	40.8085i	0.614352	+	1.42423i	−0.272492	+	0.962158i	$0.587848\pi$
$822$		0			0
$823$	−23.0619	−	5.46577i	−0.803888	−	0.190525i	−0.191923	−	0.981410i	$-0.561472\pi$
$823$	−23.0619	−	5.46577i	−0.803888	−	0.190525i	−0.611965	+	0.790885i	$0.709621\pi$
$824$	−22.2300	−	74.2535i	−0.774420	−	2.58674i
$825$		0			0
$826$	12.6957	+	1.48392i	0.441740	+	0.0516320i
$827$	−0.904516	+	5.12977i	−0.0314531	+	0.178379i	−0.996487	−	0.0837448i	$-0.973312\pi$
$827$	−0.904516	+	5.12977i	−0.0314531	+	0.178379i	0.965034	+	0.262124i	$0.0844230\pi$
$828$		0			0
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	0.999260	−	0.0384608i	$-0.0122455\pi$
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	−0.952152	+	0.305626i	$0.901134\pi$
$830$	3.05477	+	52.4484i	0.106033	+	1.82051i
$831$		0			0
$832$	−4.12143	+	9.55455i	−0.142885	+	0.331245i
$833$	−8.50616	+	4.27195i	−0.294721	+	0.148014i
$834$		0			0
$835$	5.34646	−	1.26713i	0.185022	−	0.0438510i
$836$	−71.1060	−	123.159i	−2.45925	−	4.25955i
$837$		0			0
$838$	3.56743	−	6.17897i	0.123235	−	0.213449i
$839$	−8.63105	+	28.8297i	−0.297977	+	0.995312i	0.669597	+	0.742725i	$0.266467\pi$
$839$	−8.63105	+	28.8297i	−0.297977	+	0.995312i	−0.967574	+	0.252588i	$0.918718\pi$
$840$		0			0
$841$	20.1774	+	13.2709i	0.695772	+	0.457616i
$842$	−9.36628	−	12.5811i	−0.322783	−	0.433573i
$843$		0			0
$844$	−68.1571	+	44.8277i	−2.34607	+	1.54303i
$845$	11.1787	+	4.06870i	0.384557	+	0.139967i
$846$		0			0
$847$	34.2925	−	12.4814i	1.17830	−	0.428867i
$848$	31.1810	−	41.8833i	1.07076	−	1.43828i
$849$		0			0
$850$	−15.4856	+	16.4138i	−0.531151	+	0.562987i
$851$	−13.9421	+	14.7778i	−0.477929	+	0.506575i
$852$		0			0
$853$	3.32810	−	4.47042i	0.113952	−	0.153064i	−0.741488	−	0.670966i	$-0.765879\pi$
$853$	3.32810	−	4.47042i	0.113952	−	0.153064i	0.855440	+	0.517902i	$0.173287\pi$
$854$	−8.68141	+	3.15978i	−0.297072	+	0.108125i
$855$		0			0
$856$	23.7619	+	8.64862i	0.812165	+	0.295604i
$857$	14.6309	−	9.62290i	0.499782	−	0.328712i	−0.274463	−	0.961598i	$-0.588500\pi$
$857$	14.6309	−	9.62290i	0.499782	−	0.328712i	0.774245	+	0.632886i	$0.218130\pi$
$858$		0			0
$859$	−20.0517	−	26.9341i	−0.684154	−	0.918978i	0.315396	−	0.948960i	$-0.397863\pi$
$859$	−20.0517	−	26.9341i	−0.684154	−	0.918978i	−0.999550	+	0.0299816i	$0.990455\pi$
$860$	−3.94495	−	2.59463i	−0.134522	−	0.0884763i
$861$		0			0
$862$	12.3956	−	41.4042i	0.422196	−	1.41023i
$863$	5.63576	−	9.76143i	0.191844	−	0.332283i	−0.754018	−	0.656854i	$-0.771887\pi$
$863$	5.63576	−	9.76143i	0.191844	−	0.332283i	0.945861	+	0.324571i	$0.105220\pi$
$864$		0			0
$865$	11.4933	+	19.9069i	0.390782	+	0.676855i
$866$	33.1791	−	7.86359i	1.12747	−	0.267216i
$867$		0			0
$868$	45.3647	−	22.7830i	1.53978	−	0.773306i
$869$	8.79634	−	20.3922i	0.298395	−	0.691758i
$870$		0			0
$871$	0.741772	+	12.7357i	0.0251340	+	0.431534i
$872$	6.88157	+	39.0273i	0.233039	+	1.32163i
$873$		0			0
$874$	9.30925	−	52.7954i	0.314890	−	1.78583i
$875$	−35.7636	−	4.18016i	−1.20903	−	0.141315i
$876$		0			0
$877$	−10.5547	−	35.2552i	−0.356408	−	1.19049i	−0.928824	−	0.370522i	$-0.879179\pi$
$877$	−10.5547	−	35.2552i	−0.356408	−	1.19049i	0.572416	−	0.819963i	$-0.306006\pi$
$878$	−90.5273	−	21.4554i	−3.05515	−	0.724083i
$879$		0			0
$880$	14.2676	+	33.0759i	0.480959	+	1.11499i
$881$	10.8033	+	9.06508i	0.363974	+	0.305410i	0.806372	−	0.591408i	$-0.201428\pi$
$881$	10.8033	+	9.06508i	0.363974	+	0.305410i	−0.442398	+	0.896819i	$0.645872\pi$
$882$		0			0
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	−0.970535	−	0.240961i	$-0.922538\pi$
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	0.0687683	+	0.997633i	$0.478093\pi$
$884$	−24.1262	−	12.1166i	−0.811451	−	0.407526i
$885$		0			0
$886$	−11.0652	+	1.29334i	−0.371742	+	0.0434504i
$887$	2.54514	−	43.6983i	0.0854573	−	1.46725i	−0.634336	−	0.773057i	$-0.718727\pi$
$887$	2.54514	−	43.6983i	0.0854573	−	1.46725i	0.719794	−	0.694188i	$-0.244236\pi$
$888$		0			0
$889$	−22.4010	−	23.7436i	−0.751304	−	0.796336i
$890$	−14.5535			−0.487833
$891$		0			0
$892$	−63.9539			−2.14134
$893$	−28.2092	−	29.9000i	−0.943986	−	1.00057i
$894$		0			0
$895$	−1.77557	+	30.4853i	−0.0593507	+	1.01901i
$896$	−53.6240	+	6.26775i	−1.79145	+	0.209391i
$897$		0			0
$898$	−8.17267	−	4.10447i	−0.272726	−	0.136968i
$899$	6.35325	−	5.33101i	0.211893	−	0.177799i
$900$		0			0
$901$	−22.1820	−	18.6129i	−0.738988	−	0.620085i
$902$	19.8257	+	45.9610i	0.660122	+	1.53034i
$903$		0			0
$904$	−42.3004	−	10.0254i	−1.40689	−	0.333439i
$905$	2.56482	+	8.56710i	0.0852576	+	0.284780i
$906$		0			0
$907$	16.6087	+	1.94128i	0.551482	+	0.0644590i	0.387270	−	0.921966i	$-0.373418\pi$
$907$	16.6087	+	1.94128i	0.551482	+	0.0644590i	0.164212	+	0.986425i	$0.447492\pi$
$908$	−4.62359	+	26.2217i	−0.153439	+	0.870196i
$909$		0			0
$910$	−4.14918	−	23.5311i	−0.137544	−	0.780050i
$911$	−1.11002	−	19.0583i	−0.0367765	−	0.631429i	−0.965459	−	0.260554i	$-0.916095\pi$
$911$	−1.11002	−	19.0583i	−0.0367765	−	0.631429i	0.928683	−	0.370875i	$-0.120942\pi$
$912$		0			0
$913$	−28.0678	+	65.0685i	−0.928908	+	2.15345i
$914$	−40.9612	+	20.5715i	−1.35488	+	0.680444i
$915$		0			0
$916$	38.3042	−	9.07825i	1.26561	−	0.299954i
$917$	−13.7274	−	23.7765i	−0.453319	−	0.785171i
$918$		0			0
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	−0.900591	−	0.434668i	$-0.856866\pi$
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	0.826729	+	0.562600i	$0.190199\pi$
$920$	−6.77809	+	22.6404i	−0.223467	+	0.746432i
$921$		0			0
$922$	−25.1467	−	16.5393i	−0.828164	−	0.544692i
$923$	−4.56816	−	6.13610i	−0.150363	−	0.201972i
$924$		0			0
$925$	16.9446	−	11.1447i	0.557136	−	0.366434i
$926$	−6.45541	−	2.34958i	−0.212138	−	0.0772119i
$927$		0			0
$928$	4.91493	−	1.78889i	0.161340	−	0.0587231i
$929$	24.3387	−	32.6925i	0.798526	−	1.07261i	−0.197210	−	0.980361i	$-0.563188\pi$
$929$	24.3387	−	32.6925i	0.798526	−	1.07261i	0.995736	−	0.0922458i	$-0.0294046\pi$
$930$		0			0
$931$	−15.4912	+	16.4197i	−0.507704	+	0.538135i
$932$	−61.0240	+	64.6817i	−1.99891	+	2.11872i
$933$		0			0
$934$	−46.8985	+	62.9956i	−1.53456	+	2.06128i
$935$	18.7715	−	6.83227i	0.613894	−	0.223439i
$936$		0			0
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.115640	−	0.993291i	$-0.536892\pi$
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.727060	+	0.686574i	$0.759114\pi$
$938$	−39.7796	+	26.1634i	−1.29885	+	0.854266i
$939$		0			0
$940$	20.5472	+	27.5997i	0.670176	+	0.900203i
$941$	−2.11164	−	1.38885i	−0.0688375	−	0.0452751i	0.514624	−	0.857416i	$-0.327932\pi$
$941$	−2.11164	−	1.38885i	−0.0688375	−	0.0452751i	−0.583461	+	0.812141i	$0.698302\pi$
$942$		0			0
$943$	−3.67311	+	12.2690i	−0.119613	+	0.399535i
$944$	−4.33786	+	7.51340i	−0.141185	+	0.244540i
$945$		0			0
$946$	−4.69172	−	8.12630i	−0.152541	−	0.264209i
$947$	12.4238	−	2.94449i	0.403718	−	0.0956829i	−0.0237399	−	0.999718i	$-0.507557\pi$
$947$	12.4238	−	2.94449i	0.403718	−	0.0956829i	0.427458	+	0.904035i	$0.359409\pi$
$948$		0			0
$949$	21.2954	−	10.6950i	0.691279	−	0.347173i
$950$	−21.1967	+	49.1394i	−0.687711	+	1.59429i
$951$		0			0
$952$	−3.08554	−	52.9766i	−0.100003	−	1.71698i
$953$	−1.62376	−	9.20879i	−0.0525987	−	0.298302i	0.947148	−	0.320796i	$-0.103950\pi$
$953$	−1.62376	−	9.20879i	−0.0525987	−	0.298302i	−0.999747	+	0.0224940i	$0.992839\pi$
$954$		0			0
$955$	−3.37322	+	19.1305i	−0.109155	+	0.619048i
$956$	−68.8265	−	8.04467i	−2.22601	−	0.260183i
$957$		0			0
$958$	1.99484	+	6.66324i	0.0644504	+	0.215279i
$959$	3.31732	+	0.786220i	0.107122	+	0.0253884i
$960$		0			0
$961$	−6.66071	−	15.4413i	−0.214862	−	0.498105i
$962$	27.3859	+	22.9795i	0.882958	+	0.740890i
$963$		0			0
$964$	5.34797	−	4.48748i	0.172247	−	0.144532i
$965$	4.75053	+	2.38580i	0.152925	+	0.0768018i
$966$		0			0
$967$	2.13167	−	0.249157i	0.0685500	−	0.00801235i	−0.0817488	−	0.996653i	$-0.526051\pi$
$967$	2.13167	−	0.249157i	0.0685500	−	0.00801235i	0.150299	+	0.988641i	$0.451976\pi$
$968$	−3.69299	+	63.4062i	−0.118697	+	2.03795i
$969$		0			0
$970$	−30.3371	−	32.1555i	−0.974066	−	1.03245i
$971$	18.8603			0.605255			0.302627	−	0.953109i	$-0.402136\pi$
$971$	18.8603			0.605255			0.302627	+	0.953109i	$0.402136\pi$
$972$		0			0
$973$	23.7603			0.761719
$974$	54.2748	+	57.5279i	1.73908	+	1.84331i
$975$		0			0
$976$	0.364601	−	6.25996i	0.0116706	−	0.200376i
$977$	59.7085	−	6.97892i	1.91024	−	0.223276i	0.923270	−	0.384151i	$-0.125506\pi$
$977$	59.7085	−	6.97892i	1.91024	−	0.223276i	0.986975	+	0.160876i	$0.0514319\pi$
$978$		0			0
$979$	−17.5422	−	8.81001i	−0.560650	−	0.281569i
$980$	14.4748	−	12.1458i	0.462380	−	0.387983i
$981$		0			0
$982$	67.2670	+	56.4437i	2.14657	+	1.80119i
$983$	−12.7239	−	29.4973i	−0.405829	−	0.940817i	−0.991481	−	0.130254i	$-0.958421\pi$
$983$	−12.7239	−	29.4973i	−0.405829	−	0.940817i	0.585652	−	0.810563i	$-0.300839\pi$
$984$		0			0
$985$	−7.55598	−	1.79080i	−0.240754	−	0.0570597i
$986$	−4.72125	−	15.7701i	−0.150355	−	0.502221i
$987$		0			0
$988$	−63.5941	−	7.43309i	−2.02320	−	0.236478i
$989$	0.416905	−	2.36439i	0.0132568	−	0.0751831i
$990$		0			0
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	−0.999895	−	0.0145131i	$-0.995380\pi$
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	0.934630	−	0.355622i	$-0.115731\pi$
$992$	0.520093	+	8.92965i	0.0165130	+	0.283517i
$993$		0			0
$994$	11.3082	−	26.2154i	0.358675	−	0.831503i
$995$	−21.3507	+	10.7227i	−0.676861	+	0.339933i
$996$		0			0
$997$	−41.3358	+	9.79677i	−1.30912	+	0.310267i	−0.825198	−	0.564844i	$-0.808936\pi$
$997$	−41.3358	+	9.79677i	−1.30912	+	0.310267i	−0.483922	+	0.875111i	$0.660788\pi$
$998$	9.96735	+	17.2640i	0.315511	+	0.546481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.199.1		144
3.2	odd	2		81.2.g.a.22.8	✓	144
9.2	odd	6		729.2.g.d.352.8		144
9.4	even	3		729.2.g.b.595.8		144
9.5	odd	6		729.2.g.c.595.1		144
9.7	even	3		729.2.g.a.352.1		144
81.11	odd	54		81.2.g.a.70.8	yes	144
81.16	even	27		729.2.g.a.379.1		144
81.31	even	27		6561.2.a.d.1.67		72
81.38	odd	54		729.2.g.c.136.1		144
81.43	even	27		729.2.g.b.136.8		144
81.50	odd	54		6561.2.a.c.1.6		72
81.65	odd	54		729.2.g.d.379.8		144
81.70	even	27	inner	243.2.g.a.127.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.8	✓	144	3.2	odd	2
81.2.g.a.70.8	yes	144	81.11	odd	54
243.2.g.a.127.1		144	81.70	even	27	inner
243.2.g.a.199.1		144	1.1	even	1	trivial
729.2.g.a.352.1		144	9.7	even	3
729.2.g.a.379.1		144	81.16	even	27
729.2.g.b.136.8		144	81.43	even	27
729.2.g.b.595.8		144	9.4	even	3
729.2.g.c.136.1		144	81.38	odd	54
729.2.g.c.595.1		144	9.5	odd	6
729.2.g.d.352.8		144	9.2	odd	6
729.2.g.d.379.8		144	81.65	odd	54
6561.2.a.c.1.6		72	81.50	odd	54
6561.2.a.d.1.67		72	81.31	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71221 - 1.81484i) q^{2} +(-0.245679 + 4.21814i) q^{4} +(-1.39804 + 0.163408i) q^{5} +(-2.85083 - 1.43174i) q^{7} +(4.25325 - 3.56890i) q^{8} +(2.69030 + 2.25743i) q^{10} +(1.87624 + 4.34961i) q^{11} +(2.07522 + 0.491837i) q^{13} +(2.28284 + 7.62523i) q^{14} +(-5.36597 - 0.627192i) q^{16} +(-0.520249 + 2.95048i) q^{17} +(1.23380 + 6.99724i) q^{19} +(-0.345808 - 5.93730i) q^{20} +(4.68131 - 10.8525i) q^{22} +(2.70239 - 1.35719i) q^{23} +(-2.93740 + 0.696176i) q^{25} +(-2.66061 - 4.60832i) q^{26} +(6.73968 - 11.6735i) q^{28} +(0.631591 - 2.10966i) q^{29} +(3.14652 + 2.06950i) q^{31} +(1.41830 + 1.90511i) q^{32} +(6.24541 - 4.10767i) q^{34} +(4.21955 + 1.53579i) q^{35} +(-6.31317 + 2.29781i) q^{37} +(10.5863 - 14.2199i) q^{38} +(-5.36304 + 5.68449i) q^{40} +(-2.90628 + 3.08048i) q^{41} +(0.474097 - 0.636822i) q^{43} +(-18.8082 + 6.84563i) q^{44} +(-7.09015 - 2.58060i) q^{46} +(-4.83370 + 3.17917i) q^{47} +(1.89725 + 2.54844i) q^{49} +(6.29289 + 4.13890i) q^{50} +(-2.58448 + 8.63275i) q^{52} +(-4.83254 + 8.37020i) q^{53} +(-3.33382 - 5.77435i) q^{55} +(-17.2350 + 4.08478i) q^{56} +(-4.91010 + 2.46595i) q^{58} +(0.636054 - 1.47454i) q^{59} +(0.0674875 + 1.15872i) q^{61} +(-1.63170 - 9.25383i) q^{62} +(-0.847235 + 4.80491i) q^{64} +(-2.98162 - 0.348502i) q^{65} +(1.71558 + 5.73045i) q^{67} +(-12.3177 - 2.91935i) q^{68} +(-4.43754 - 10.2874i) q^{70} +(-2.74773 - 2.30562i) q^{71} +(8.55952 - 7.18229i) q^{73} +(14.9796 + 7.52304i) q^{74} +(-29.8185 + 3.48528i) q^{76} +(0.878675 - 15.0863i) q^{77} +(-3.21730 - 3.41014i) q^{79} +7.60435 q^{80} +10.5667 q^{82} +(10.2659 + 10.8812i) q^{83} +(0.245199 - 4.20991i) q^{85} +(-1.96748 + 0.229966i) q^{86} +(23.5034 + 11.8038i) q^{88} +(-3.17449 + 2.66371i) q^{89} +(-5.21193 - 4.37333i) q^{91} +(5.06091 + 11.7325i) q^{92} +(14.0460 + 3.32896i) q^{94} +(-2.86831 - 9.58083i) q^{95} +(-12.5027 - 1.46135i) q^{97} +(1.37652 - 7.80666i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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